The state-of-the-art physics consists of two irreconcilable branches, i.e., the quantum theory and the general relativity, which work well in their own territories, independently. However, what are quantum and spacetime after all? The key question was never addressed, satisfactorily. In this work, we describe a possibility to reformulate the quantum theory in the Minkowski spacetime from the viewpoint of classic physics in the Euclidean spacetime, i.e., classic mechanics and stochastic process theory. We show that quantum theory and Minkowski spacetime may connect with each other and emerge from a single fundamental entity.
Quantum theory and relativity are the pillar theories on which our understanding of physics is based. Poincar\'e invariance is a fundamental physical principle stating that the experimental results must be the same in all inertial reference frames in Minkowski spacetime. It is a basic condition imposed on quantum theory in order to construct quantum field theories, hence, it plays a fundamental role in the standard model of particle physics too. As is well known, Minkowski spacetime follows from clear physical principles, like the relativity principle and the invariance of the speed of light. Here we reproduce such a derivation but leave the number of spatial dimensions
n as a free variable. Then, assuming that spacetime is Minkowski in
1+n dimensions and within the framework of general probabilistic theories, we reconstruct the qubit Bloch ball and finite dimensional quantum theory, and obtain that the number of spatial dimensions must be
n=3, from Poincar\'e invariance and other physical postulates. Our results suggest a fundamental physical connection between spacetime and quantum theory.
This paper advances the core thesis that the speed of light is the limit of physical quantities, not the limit of spacetime quantities. The "superluminal" correlations of quantum entanglement and the "superluminal" recession of distant galaxies in cosmic expansion are not violations of relativity, but rather because these two phenomena belong to the category of spacetime quantities and fall outside the jurisdiction of the speed of light. Through the methodology of "hierarchical reclassification," this paper separates physical quantities (matter, energy, signals, causal chains) from spacetime quantities (spacetime structure, expansion, connectivity, topological relations), pointing out that the definition of velocity (m/s) presupposes "matter moving through space"; when the object of discussion is spacetime itself, the concept of "velocity" no longer applies. This paper further clarifies that there is no fundamental contradiction between relativity and quantum mechanics requiring "unification"—they describe effective laws at different levels (the L4 physical level and the L1–L2 quantum level). The "superluminal paradox" that has long troubled physics is, in essence, a result of category misplacement.